Hamilton-Jacobi Equation for Brans-Dicke Theory and Its Long-wavelength Solution

TL;DR

This paper solves the Hamilton-Jacobi equation for Brans-Dicke theory using a long-wavelength approximation, analyzing the evolution of inhomogeneities in different cosmological scenarios.

Contribution

It provides a novel solution to the Hamilton-Jacobi equation in Brans-Dicke theory and explores the nonlinear evolution of inhomogeneities in cosmology.

Findings

Inhomogeneities grow in dust fluid scenarios.

Inhomogeneities decay with a cosmological constant.

Density perturbations and gravitational constant behave similarly.

Abstract

Hamilton-Jacobi equation for Brans-Dicke theory is solved by using a long-wavelength approximation. We examine the non-linear evolution of the inhomogeneities in the dust fluid case and the cosmological constant case. In the case of dust fluid, it turns out that the inhomogeneities of space-time grow. In the case of cosmological constant, the inhomogeneities decay, which is consistent with the cosmic no hair conjecture. The inhomogeneities of the density perturbation and the gravitational constant behave similarly with that of space-time.